Dimensioning of Fractal Fracture on a Concrete Slab

Abstract

What is presented here is a methodology that allows to study fractures in any material, especially in concrete elements. The importance lies in the moment in which the fracture that occurs in a structural element (slab in our case study) causes a negative effect on its structural behavior. Traditionally, its study is developed from the perspective of fracture mechanics, with which the energy at the tip of the crack or fracture is calculated, and it cannot go further. But the combination of the theories of fracture mechanics and fractal geometry allows us to obtain the patterns of its behavior in the future. Thus, the research was based on tests made on structural elements of concrete, from a slab led to structural failure and choosing a fracture. This was vectorized in order to obtain a fractal axis, which was called state 0, taking three parts or sections of that state and repeating them on a smaller scale. Subsequently, the research was based on five of the methods used for the study and calculation of the fractal dimension: box dimension, perimeter-area dimension, information dimension, mass dimension, and ruler dimension. Most of the fractal dimensions obtained under these methods were similar to each other.